You are describin a peripheralising effect of your low back pain - this is quite common in a discogenic pain. Your mechanism of injury isn't specifically typical of a disc pathology but your symptoms certainly seem to be.
Back pain will usually resolve within 6 weeks - that said that doesn't mean you can't have physio early on.
I suggest you go back to the doctor for a physio referral - if possible look for a therapist that is mckenzie trained (they understand disc pain quite well).
We need more information and an examination to make a true diagnosis and advise exercises through the forum.

You need to visit a physio as the cause of your pain doesn't have to be related to a disc problem - you could be looking at a stability problem or Wikipedia reference-linkSIJ problem - it may be possible you have a disc prolapse even which would require a Wikipedia reference-linkMRI to confirm.

Seek further assessment and help. good luck to you